cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A100003 Prime numbers p such that the concatenation of all odd primes up through p in decreasing order is prime.

Original entry on oeis.org

3, 5, 17, 89, 383, 8831
Offset: 1

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Author

Farideh Firoozbakht, Nov 06 2004

Keywords

Comments

Next term is greater than 4400th prime and the prime corresponding to the next term has more than 20000 digits. Number of digits of primes corresponding to the six known terms of the sequence are respectively 1, 2, 9, 43, 198, 4202.
We can see the prime corresponding to 383 (the 5th term of the sequence) in the page related to puzzle 8 of the website of Carlos Rivera.
a(7) > prime(28800) = 335033. - Giovanni Resta, Apr 01 2013

Examples

			17 is in the sequence because 17.13.11.7.5.3 is prime (dot between numbers means concatenation).

Links

Crossrefs

Cf. A046284, A099070, A099071, A099073.
The actual prime concatenations in A092448 and the original concatenations in A092447. - Dmitry Kamenetsky, Mar 02 2009

Programs

  • Mathematica
    Do[If[PrimeQ[(v={};Do[v=Join[v, IntegerDigits[Prime[n-j+1]]], {j, n-1}];FromDigits[v])], Print[Prime[n]]], {n, 2, 4413}]
Prime[#]&/@Select[Range[100],PrimeQ[FromDigits[Flatten[IntegerDigits/@ Prime[Range[#,2,-1]]]]]&] (* To generate a(6) increase the Range by 1000, but the program will run a long time. *) (* Harvey P. Dale, Nov 27 2015 *)

A099071 Composite numbers k such that the concatenation of all nonprime positive integers up to k in decreasing order is prime.

Original entry on oeis.org

4, 6, 8, 9, 26, 1752
Offset: 1

Views

Author

Farideh Firoozbakht, Nov 06 2004

Keywords

Comments

The terms of this sequence are composite terms of the sequence A099070 with the same order. Next term is greater than 6000 and the prime corresponding to the next term has more than 20000 digits. Number of digits of primes corresponding to the six known terms of the sequence are respectively 2, 3, 4, 5, 29, and 5010.

Examples

			26 is a term: 26 is composite; nonprimes up to 26 are 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26; and 26252422212018161514121098641 is prime.

Links

Crossrefs

Cf. A099070, A100003, A046284.

Programs

  • Mathematica
    Do[If[ !PrimeQ[n]&&PrimeQ[(v={};Do[If[ !PrimeQ[n+1-j], v=Join[v, IntegerDigits[n+1-j]]], {j, n}];FromDigits[v])], Print[n]], {n, 6013}]
cnpQ[n_]:=PrimeQ[FromDigits[Flatten[IntegerDigits/@Select[Range[n,1,-1],!PrimeQ[#]&]]]]; Select[Range[1800],!PrimeQ[#]&&cnpQ[#]&] (* Harvey P. Dale, Jul 19 2020 *)

A099073 Numbers k such that the concatenation of the first k-1 odd primes in decreasing order is prime.

Original entry on oeis.org

2, 3, 7, 24, 76, 1100
Offset: 1

Views

Author

Farideh Firoozbakht, Nov 06 2004

Keywords

Comments

A100003(n) = prime(a(n)). Next term is greater than 4500 and the prime corresponding to the next term has more than 21000 digits. Number of digits of primes corresponding to the six known terms of the sequence are respectively 1, 2, 9, 43, 198, and 4202. There is no known prime formed by concatenation of the first k odd primes in increasing order for 1 < k < 2250.
a(7) > 20000. - Michael S. Branicky, Nov 25 2024

Examples

			7 is in the sequence because the first 6 odd primes are 3,5,7,11,13,17 and 17.13.11.7.5.3 is prime (dot between numbers means concatenation).

Links

Crossrefs

Cf. A046035, A099070, A099071.

Programs

  • Mathematica
    Do[If[PrimeQ[(v={};Do[v=Join[v, IntegerDigits[Prime[n-j+1]]], {j, n-1}];FromDigits[v])], Print[n]], {n, 2, 4500}]
Select[Range[1100],PrimeQ[FromDigits[Flatten[IntegerDigits/@ Reverse[ Prime[ Range[ 2,#]]]]]]&] (* Harvey P. Dale, Nov 12 2017 *)
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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